Results 41 to 50 of about 4,035 (167)
Color-critical graphs and hypergraphs
Journal of Combinatorial Theory, Series B, 1974 Abstract The main purpose of this paper is to present a technique for obtaining constructions of color-critical graphs. The technique consists in reducing color-critical hypergraphs to color-critical graphs, and the constructions obtained generalize and unify known constructions.
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Quantum‐Enhanced Simulated Annealing Using Rydberg Atoms
Advanced Quantum Technologies, EarlyView.This study experimentally demonstrates that a Rydberg hybrid quantum‐classical algorithm, termed as quantum‐enhanced simulated annealing (QESA), provides a computational time advantage over a classical standalone simulated annealing (SA). This scatter plot represents the comparison of QESA versus SA for the 924 graphs with the sizes N=60$N=60$, 80 and ...
Seokho Jeong, Juyoung Park, Jaewook Ahn
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Journal of Graph Theory, Volume 110, Issue 1, Page 82-91, September 2025.ABSTRACT An inversion of a tournament T is obtained by reversing the direction of all edges with both endpoints in some set of vertices. Let inv k ( T ) be the minimum length of a sequence of inversions using sets of size at most k that result in the transitive tournament.
Raphael Yuster
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Color-critical graphs and hypergraphs with few edges and no short cycles
Discrete Mathematics, 1998 An \(r\)-coloring of a hypergraph \((V, {\mathcal G})\) with vertex set \(V\) and edge set \({\mathcal G}\) is a coloring of its vertices with at most \(r\) colors such that each edge is incident with at least two vertices of different colors. \((V, {\mathcal G})\) is \(r\)-chromatic if \(r\) is the smallest integer for which \((V, {\mathcal G})\) is \(
Donovan R. Hare, Bing Zhou, H. L. Abbott
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A Sharper Ramsey Theorem for Constrained Drawings
Journal of Graph Theory, Volume 109, Issue 4, Page 401-411, August 2025.ABSTRACT Given a graph G and a collection C of subsets of R d indexed by the subsets of vertices of G, a constrained drawing of G is a drawing where each edge is drawn inside some set from C, in such a way that nonadjacent edges are drawn in sets with disjoint indices. In this paper we prove a Ramsey‐type result for such drawings.
Pavel Paták
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Distributed Deterministic Edge Coloring using Bounded Neighborhood Independence [PDF]
, 2010 We study the {edge-coloring} problem in the message-passing model of distributed computing. This is one of the most fundamental and well-studied problems in this area.
Barenboim, Leonid, Elkin, Michael
core
Deterministic Distributed Edge-Coloring via Hypergraph Maximal Matching
, 2017 We present a deterministic distributed algorithm that computes a $(2\Delta-1)$-edge-coloring, or even list-edge-coloring, in any $n$-node graph with maximum degree $\Delta$, in $O(\log^7 \Delta \log n)$ rounds.
Fischer, Manuela +2 more
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Sequentially Constrained Hamilton Cycles in Random Graphs
Random Structures &Algorithms, Volume 67, Issue 1, August 2025.ABSTRACT We discuss the existence of Hamilton cycles in the random graph Gn,p$$ {G}_{n,p} $$ where there are restrictions caused by (i) coloring sequences, (ii) a subset of vertices must occur in a specific order, and (iii) there is a bound on the number of inversions in the associated permutation.
Alan Frieze, Wesley Pegden
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Canonical colourings in random graphs
Journal of the London Mathematical Society, Volume 112, Issue 2, August 2025.Abstract Rödl and Ruciński (J. Amer. Math. Soc. 8 (1995), 917–942) established Ramsey's theorem for random graphs. In particular, for fixed integers r$r$, ℓ⩾2$\ell \geqslant 2$ they proved that p̂Kℓ,r(n)=n−2ℓ+1$\hat{p}_{K_\ell,r}(n)=n^{-\frac{2}{\ell +1}}$ is a threshold for the Ramsey property that every r$r$‐colouring of the edges of the binomial ...
Nina Kamčev, Mathias Schacht
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Color-bounded hypergraphs, V: host graphs and subdivisions
Discussiones Mathematicae Graph Theory, 2011 A color-bounded hypergraph is a hypergraph (set system) with ver- tex set X and edge set e = {E1, . . . ,Em}, together with integers si and ti satisfying 1 ≤ si ≤ ti ≤ |E1| for each i = 1, . . . ,m. A vertex coloring φ is proper if for every i, the number of colors occurring in edge 1 satisfies si ≤ |φ(Ei)| ≤ t i.
Zsolt Tuza +2 more
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